Suppose S and T are mutually exclusive events. Find P(S or T) if P(S) = 29% and P(T) = 49%.
What equation would I use for this question?
What if they were not mutually exclusive?
If S and T are mutually exclusive events, it means that they cannot occur at the same time. In such cases, to find the probability of either event S or T occurring, you would simply add the probabilities of each event:
P(S or T) = P(S) + P(T)
So, in this case, to find the probability of either event S or T occurring, you would add 29% and 49%:
P(S or T) = 29% + 49%
If S and T were not mutually exclusive events and could occur concurrently, to find the probability of either event S or T occurring, you would use the principle of inclusion-exclusion. The formula is:
P(S or T) = P(S) + P(T) - P(S and T)
So, in this case, to find the probability of either event S or T occurring, you would have to know the additional information of the probability of both events S and T occurring simultaneously, denoted as P(S and T).
To find the probability of two mutually exclusive events, you can use the formula:
P(S or T) = P(S) + P(T)
In this case, since S and T are mutually exclusive, they cannot occur at the same time. Therefore, we can add their individual probabilities to find the probability of either event happening.
Using the given information:
P(S) = 29%
P(T) = 49%
To find P(S or T), you substitute the values into the equation:
P(S or T) = P(S) + P(T)
P(S or T) = 29% + 49%
P(S or T) = 78%
Therefore, the probability of either S or T occurring is 78%.
Now, if S and T were not mutually exclusive, you would use the formula for the probability of the union of two events:
P(S or T) = P(S) + P(T) - P(S and T)
In this case, you would deduct the probability of both events occurring simultaneously.